TY - JOUR

T1 - On solitons, compactons, and Lagrange maps

AU - Rosenau, Philip

PY - 1996/2/26

Y1 - 1996/2/26

N2 - Two local conservation laws of the K(m, n) equation, u1 ± (um)x + (un)xxx = 0, are used to define two Lagrange-type transformations into mass and momentum space. These mappings help to identify new integrable cases (K(-1, -2), K(-2, -2), K(3/2, - 1/2)), transform conventional solitary waves into compactons - solitary waves on compactum - and relate certain soliton-carrying systems with compacton-carrying systems. Integrable equations are transformed into new integrable equations and interaction of N-solitons of the, say, m-KdV (m = 3, n = 1) is thus projected into an interaction in a compact domain from which N ordered stationary compactons emerge. The interaction of traveling compactons is the image of super-imposed equilibria of the corresponding soliton equation. For m = n + 2, the potential form of the K(m, n) equation may also be cast into a conserved form and thus transformed, yielding generalized Dym and Wadati equations and two new integrable cases. It is shown that r1 + (1-r2)3/2(rxy + r)x = 0 is integrable and supports compact kinks.

AB - Two local conservation laws of the K(m, n) equation, u1 ± (um)x + (un)xxx = 0, are used to define two Lagrange-type transformations into mass and momentum space. These mappings help to identify new integrable cases (K(-1, -2), K(-2, -2), K(3/2, - 1/2)), transform conventional solitary waves into compactons - solitary waves on compactum - and relate certain soliton-carrying systems with compacton-carrying systems. Integrable equations are transformed into new integrable equations and interaction of N-solitons of the, say, m-KdV (m = 3, n = 1) is thus projected into an interaction in a compact domain from which N ordered stationary compactons emerge. The interaction of traveling compactons is the image of super-imposed equilibria of the corresponding soliton equation. For m = n + 2, the potential form of the K(m, n) equation may also be cast into a conserved form and thus transformed, yielding generalized Dym and Wadati equations and two new integrable cases. It is shown that r1 + (1-r2)3/2(rxy + r)x = 0 is integrable and supports compact kinks.

UR - http://www.scopus.com/inward/record.url?scp=0001026321&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(95)00933-7

DO - 10.1016/0375-9601(95)00933-7

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AN - SCOPUS:0001026321

SN - 0375-9601

VL - 211

SP - 265

EP - 275

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5

ER -